Question

Last year 1 kg of tea and 3 kg of sugar together cost Rs 96. This year, the rates of tea increased by
15% and that of sugar by 10%. So the amount of tea and sugar now cost Rs. 108.60. Find the per kg
rates of tea & sugar last year.

Answer 1

The rate of tea is Rs 60 per kg and the rate of sugar is Rs 12 per kg.

Step-by-step explanation:

We are given that last year 1 kg of tea and 3 kg of sugar together cost Rs 96. This year, the rates of tea increased by  15% and that of sugar by 10%. So the amount of tea and sugar now cost Rs. 108.60.

Let the rate of tea be 'Rs x per kg' and the rate of sugar be 'Rs y per kg'.

• The first condition states that last year 1 kg of tea and 3 kg of sugar together cost Rs 96, that is;

                               $x+3y=96$

                                $x=96-3y$  ------------ [Equation 1]

• The second condition states that this year, the rates of tea increased by  15% and that of sugar by 10%. So the amount of tea and sugar now cost Rs. 108.60, that is;

So, this year rate of tea =  $x + (\frac{15}{100} \times x )$

                                       =  $x+\frac{15x}{100} =\frac{115x}{100}$

Also, this year rate of sugar =  $3y + (\frac{10}{100} \times 3y )$

                                              =  $3y+\frac{10\times 3y}{100} =\frac{330y}{100}$

Now, the equation so formed is;

                              $\frac{115x}{100}+\frac{330y}{100} = 108.60$

                              $115x}+330y= 10860$

                              $23x}+66y= 2172$     {taking 5 common from both sides}

                              $23(96-3y)+66y= 2172$     {using equation 1}

                              $2208-69y+66y= 2172$

                              $2208-3y= 2172$

                               $3y= 2208-2172$

                                $y=\frac{36}{3} = 12$

Now, putting value oy y in equation 1 we get;

                               $x=96-3y$

                                $x = 96 - 36 = 60$

So, the per kg rates of tea is Rs 60 per kg and that of sugar is Rs 12 per kg.

Answer 2

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